Nature of the Spin Dynamics and1/3Magnetization Plateau in Azurite

We present a specific heat and inelastic neutron scattering study in magnetic fields up into the $1/3$ magnetization plateau phase of the diamond chain compound azurite ${\mathrm{Cu}}_3({\mathrm{CO}}_3{)}_2(\mathrm{OH}{)}_2$. We establish that the magnetization plateau is a dimer-monomer state, i.e., consisting of a chain of $S=1/2$ monomers, which are separated by $S=0$ dimers on the diamond chain backbone. The effective spin couplings $J_{\mathrm{mono}}/k_B=10.1(2)\mathrm{K}$ and $J_{\mathrm{dimer}}/k_B=1.8(1)\mathrm{K}$ are derived from the monomer and dimer dispersions. They are associated to microscopic couplings $J_1/k_B=1(2)\mathrm{K}$, $J_2/k_B=55(5)\mathrm{K}$ and a ferromagnetic $J_3/k_B=-20(5)\mathrm{K}$, possibly as result of $d_{z^2}$ orbitals in the Cu-O bonds providing superexchange (SE) pathways with $J_{\mathrm{SE}}=6.5\mathrm{K}$.